# DIVIDING A POLYNOMIAL BY A BINOMIAL

Divide the given polynomial using long division. Write your answer in fraction form.

Problem 1 :

(2x5 – 15x3 – 9x2 + 11x + 12) ÷ (x + 2)

Solution

Problem 2 :

(x4 – x3 – 19x2 - 3x - 19) ÷ (x - 5)

Solution

Problem 3 :

(10x4 – 4x3 + 14x2 - 14x - 16) ÷ (2x - 2)

Solution

Problem 4 :

(9x5 – 9x4 – x3 - 12x2 + x - 11) ÷ (3x - 5)

Solution

Problem 5 :

(16x4 + 4x3 + 2x2 - 21x + 7) ÷ (4x - 1)

Solution

Problem 6 :

(6x5 + 21x4 – 14x3 - 8x2 + x - 6) ÷ (x + 4)

Solution

1)  Quotient = 2x4 – 4x3 – 7x2 + 5x + 1

Remainder = 10

Fraction form :

2)  Quotient = x3 + 4x2 + x + 2

Remainder = -9

Fraction form :

3)  Quotient = 5x3 + 3x2 + 10x + 3

Remainder = -5

Fraction form :

4)  Quotient = 3x4 + 2x3 + 3x2 + x + 2

Remainder = -1

Fraction form :

5)  Quotient = 4x3 + 2x2 + x - 5

Remainder = 2

Fraction form :

6)  Quotient = 6x4 - 3x3 - 2x2 + 0x + 1

Remainder = -10

Fraction form :

Use synthetic division to divide the polynomials given below, then find the quotient and remainder.

Problem 1 :

(x² + 8x + 1) ÷ (x - 4)

Solution

Problem 2 :

(4x² - 13x - 5) ÷ (x - 2)

Solution

Problem 3 :

(2x² - x + 7) ÷ (x + 5)

Solution

Problem 4 :

(x³ - 4x + 6) ÷ (x + 3)

Solution

Problem 5 :

(x² + 9) ÷ (x - 3)

Solution

Problem 6 :

(3x³ - 5x² - 2) ÷ (x - 1)

Solution

Problem 7 :

(x4 – 5x³ - 8x² + 13x - 12) ÷ (x - 6)

Solution

Problem 8 :

(x4 + 4x³ + 16x - 35) ÷ (x + 5)

Solution

1)  quotient is x + 12 and remainder is 49.

2)  quotient is 4x - 5 and remainder is -5

3)  quotient is 2x - 11 and remainder is 62.

4)  quotient is x² - 3x + 5 and remainder is -9

5)  quotient is x + 3 and remainder is 18

6) quotient is 3x² - 2x - 2 and remainder is -4

7)  quotient is x³ + x² - 2x + 1 and remainder is -6

8)  quotient is x³ - x² + 5x - 9 and remainder is 10.

Problem 1 :

Without performing division, find the remainder when

x3 + 2x- 7x + 5 is divided by x - 1

Solution

Problem 2 :

Without performing division, find the remainder when

x4 - 2x2 + 3x - 1 is divided by x + 2

Solution

Problem 3 :

Find a given that:

when x3 - 2x + a is divided by x - 2, the remainder is 7.

Solution

Problem 4 :

Find a given that:

when 2x3 + x2 + ax - 5 is divided by x + 1, the remainder is -8

Solution

Problem 5 :

Find a and b given that when x3 + 2x2 + ax + b is divided by x - 1 the remainder is 4, and when divided by x + 2 the remainder is 16.

Solution

Problem 6 :

2xn + ax2 - 6 leaves a remainder of -7 when divided by x - 1, and 129 when divided by x + 3. Find a and n given that n∈Z+.

Solution

Problem 7 :

When P(z) is divided by z2 - 3z + 2 the remainder is 4z - 7. Find the remainder when P(z) is divided by:

a. z - 1    b. z - 2

Solution

Problem 8 :

When P(z) is divided by z + 1 the remainder is -8 and when divided by z - 3 the remainder is 4. Find the remainder when P(z) is divided by (z - 3) (z + 1).

Solution

1) The remainder is 1.

2) The remainder is 1.

3) a = 3

4) The value of a is 2.

5)  So, the values of a and b is -5 and 6.

6)  The values of a and n is -3 and 4.

7)  a) P(1) = -3      b) P(2) = 1

8)  remainder is 3z - 5.

## Recent Articles 1. ### Solving Direct and Inverse Proportion Word Problems Worksheet

Sep 22, 23 08:41 AM

Solving Direct and Inverse Proportion Word Problems Worksheet

2. ### Round the Decimals to the Nearest Indicated Place Value

Sep 22, 23 06:13 AM

Round the Decimals to the Nearest Indicated Place Value